Known power plants can include several units, each having a set of equipment contributing to different stages of power generation. Such equipment can include for example, boilers, steam turbines and electrical generators. For the optimal running of the power plant, an important aspect can be optimal load scheduling between the different units and the respective equipment in order to meet a given power demand.
Load scheduling can have a major impact on productivity of the power generation process. A purpose of load scheduling is to minimize the power production time and/or costs, by deciding the timing, values etc. of different operating parameters for each piece of equipment in order to meet the power demand effectively and efficiently. The load scheduling can be optimized by an optimizer in the power plant control system.
A goal for the optimization exercise, for example, can be to express cost minimization as an objective function for the optimization problem. The optimization method can solve such an objective function within identified constraints. Almost all of the operational parameters can be expressed as a cost function and the optimizer can be deployed to solve the cost function associated with a variety of operations and their consequences (e.g. penalty for not meeting the demand). The solution from the optimizer can provide setpoints for the various operations to achieve desired optimized results.
The optimizer can use techniques suct as Non Linear Programming (NLP), Mixed Integer Linear Programming (MILP), Mixed Integer Non Linear Programming (MINLP), etc to solve the objective function.
In the formulation of an objective function, it can be desirable to include as many terms as possible (fuel cost, emission reduction cost, start-up and shutdown cost, ageing cost, maintenance cost, penalty cost) for consideration in the objective function in an effort to optimize the work of everything possible. When several such terms are considered in the objective function formulation, the solving of the objective function can become difficult as there is reduction in the degree of freedom to make adjustments in operating parameters (e.g., setpoints for different equipment), in order to achieve an optimal solution for the power plant. The number of terms to be considered for a particular objective function can be based on how the process control system has been designed and the values of constraints. If the number of terms is greater (e.g., it considers almost all possible aspects of the power plant in one go or has very tight constraints) then there is a possibility that the objective function may not have a solution. It may be noted that the issue of no solution as described herein may also occur when there are conditions that are not considered in the power plant model or not controllable in the power plant from the results of the optimizer.
Currently, in situations where the objective function is not solved within a reasonable time given a set of constraints, the power plant can be operated in a sub-optimal way. In addition to no-solution situations, there are other situations where one is unsure if the optimized solution is the best solution (e.g., the solution identified is the best among the multiple solutions available or is the most suitable to operate the plant in stable manner even if the solution appears to be slightly sub-optimal). More often, one does not know if there were different constraint values, and whether a better solution could have been possible.
The present disclosure describes a method which can identify and treat such situations so that the optimizer provides an acceptable solution in a defined manner. More specifically the present disclosure describes a system and method which can solve an objective function for a power plant operation by identifying and relaxing some constraints.